which line is perpendicular to a line that has a slope of $\frac{1}{2}$?

line ab
line cd
line fg
line hj

Question

which line is perpendicular to a line that has a slope of $\frac{1}{2}$?

line ab
line cd
line fg
line hj

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Line Equations", "Slope of a Line" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Perpendicular Line Equations" ] } ## Determine the required perpendicular slope Using the *Perpendicular Line Equations* knowledge point $$ m_{\perp} = -\frac{1}{m} = -\frac{1}{1/2} = -2 $$ ## Calculate the slope of each line on the graph Using the *Slope of a Line* knowledge point $$ \begin{aligned} &\text{line } AB \text{ passes through } (-5, -2) \text{ and } (4, 2): m_{AB} = \frac{2 - (-2)}{4 - (-5)} = \frac{4}{9}\ &\text{line } CD \text{ passes through } (-4, 1) \text{ and } (4, -4): m_{CD} = \frac{-4 - 1}{4 - (-4)} = -\frac{5}{8}\ &\text{line } FG \text{ passes through } (-3, -4) \text{ and } (1, 4): m_{FG} = \frac{4 - (-4)}{1 - (-3)} = \frac{8}{4} = 2\ &\text{line } HJ \text{ passes through } (-1, 3) \text{ and } (1, -1): m_{HJ} = \frac{-1 - 3}{1 - (-1)} = \frac{-4}{2} = -2 \end{aligned} $$ ## Identify the matching line The line with a slope of $-2$ is line $HJ$.

line AB

line CD

line FG

line HJ

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Line Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the required perpendicular slope

Calculate the slope of each line on the graph

Identify the matching line

Answer: